It is generally known that polyurethane foams can be manufactured using water as a blowing agent. The reaction of an isocyanate group with water yields an urea group and evolves carbon dioxide gas, acting as the agent responsible for the foaming action. The presence of urea groups, however, hardens the foam and leads to poor compression set values. In response to this problem, polyphenylene polymethylene polyisocyanate (polymeric-MDI) has been added to improve compression set; but the improvement has come at the expense of other physical properties, such as elongation, tear strength, and tensile strength. Therefore, the inventors herein have sought to make a water-blown polyurethane integral skin foam which simultaneously possesses good compression set, elongation, tear strength, and tensile strength comparable to a CFC-blown integral skin polyurethane foam, and to formulate a system that processes well, is not sensitive to minor processing conditions, and demolds quickly.